Preface
1 Introduction
1．1 A Robot's Arm
1．2 The Configuration Space of Two Electrons
1．3 State Spaces and Fiber Bundles
1．4 Further Examples
1．5 Compact Surfaces
1．6 Higher Dimensions
2 Smooth Manifolds
2．1 Topological Manifolds
2．2 Smooth Structures
2．3 Maximal Atlases
2．4 Smooth Maps
2．5 Submanifolds
2．6 Products and Sums
3 The Tangent Space
3．1 Germs
3．2 Smooth Bump Functions
3．3 The Tangent Space
3．4 The Cotangent Space
3．5 Derivations
4 Regular Values
4．1 The Rank
4．2 The Inverse Function Theorem
4．3 The Rank Theorem
4．4 Regular Values
4．5 Transversality
4．6 Sard's Theorem
4．7 Immersions and Imbeddings
5 Vector Bundles
5．1 Topological Vector Bundles
5．2 Transition Functions
5．3 Smooth Vector Bundles
5．4 Pre-vector Bundles
5．5 The Tangent Bundle
5．6 The Cotangent Bundle
……
6 Constructions on Vector Bundles
7 Integrability
8 Local Phenomena that Go Global
Appendix A Point Set Topology
References
Index
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